FR3096129A1 - method of geolocation of platforms moving in formation, computer program product and associated geolocation module - Google Patents

Abstract

Method for geolocation of platforms moving in formation, computer program product and associated geolocation module This method comprising the following steps implemented on each acquisition of a set of measurements, the set of measurements comprising local measurements relating to each of the platforms and of the distance measurements between each pair of platforms: - temporal alignment (120) of the measurements of the set of measurements to obtain a prediction of each measurement at a future instant tk + 1; - determination (140) of navigation data relating to all the platforms at the instant tk + 1 from the predictions of the measurements at the instant tk + 1; - updating (130) of the predictions of each local measurement at the instant tk + 1 or of the navigation data relating to all the platforms at the instant tk + 1; - composition (150) of a next state vector from navigation data relating to all platforms at time tk + 1. Figure for abstract: figure 3

Description

Process for the geolocation of platforms moving in formation, computer program product and associated geolocation module

The present invention relates to a method for geolocating platforms moving in formation.

The present invention also relates to an associated computer program product and geolocation module.

“Platform” means any device, in particular a motorized device, capable of moving in space, in particular in formation with other devices. Thus, an aircraft (plane, helicopter, drone, etc.), a boat, a railway vehicle or an automobile are examples of such a device.

By "movement in formation", we understand the way in which a plurality of machines move in proximity, the notion of proximity depending on the nature of the machines and the formation. This displacement can be carried out, for example, by keeping distances substantially constant between each pair of machines or else by varying these distances according, for example, to external events or predetermined rules. The machines thus form a structure which is sometimes called a swarm.

Methods for the geolocation of aircraft flying in formation are known in the state of the art.

These methods generally make it possible to implement so-called collaborative navigation. Such a type of navigation consists in exchanging navigation information between the aircraft via for example a radio link. After an analysis of all the information transmitted, it is possible to precisely obtain the position of each of the aircraft.

Thus, according to known examples, each aircraft generally has a GNSS (Global Navigation Satellite System) receiver making it possible to obtain an absolute position of this aircraft by using a satellite positioning module.

At least some aircraft are also capable of measuring the distance between them by implementing a telemetry technique.

This technique makes it possible to measure distances between pairs of aircraft by exploiting, for example, a radio link or any other link available between them.

In particular, to do this, one of the aircraft of a pair of aircraft transmits a signal of a predetermined type in the radio link formed with the other aircraft of the pair. This other aircraft also responds to this signal with a signal of a predetermined type which is then received by the first aircraft. Thus, by measuring the time between the instant of transmission of the signal by the first aircraft and the instant of reception of the response to this signal, it is possible to determine the distance separating the two aircraft.

There also exist goniometry techniques making it possible to determine relative angles between different aircraft by analyzing the direction from which the radio signals of these aircraft originate.

It is therefore possible to combine information received via GNSS sensors with telemetry measurements and possibly goniometry measurements, in order to deduce the position of each of the aircraft in a particularly precise manner.

However, in the event of denial of the GNSS signals (in particular cases of jamming or various cases of breakdowns), the determination of a precise position of each of the aircraft flying in formation becomes particularly complicated.

To overcome this difficulty, methods of the state of the art propose to determine the position of each of the aircraft by using other measuring instruments available on board such as an inertial unit in particular.

The measurements from these instruments are then combined with distance measurements between different pairs of aircraft obtained by implementing a telemetry technique.

The different measurements are then buffered and merged at the end of each buffering cycle in order to deduce the position of each of the aircraft.

However, for platforms with very high mobility, that is to say for platforms having large relative displacements in a short time, the buffered measurements (position and/or telemetry and/or goniometry measurements) cannot no longer be considered as still valid at the end of the cycle due to the movements of the platforms between the instant of the measurement and the instant of the end of the cycle.

In addition, distance measurements that take place over a certain period of time may have insufficient precision and can no longer be used as is.

Indeed, in most telemetry techniques, it is often assumed that the distance between each pair of platforms remains substantially unchanged between the instant of transmission of the predetermined type signal and the instant of reception of the response signal. However, for platforms with high mobility, this assumption can no longer give reliable results.

Thus, not only can the measurements buffered over a cycle not be used as they are, but measurements of the distance determined between pairs of platforms with high mobility cannot be used in a conventional manner to deduce the positions of the platforms within 'a training.

The aim of the present invention is to remedy these drawbacks and therefore to propose a method making it possible both to merge the measurements with a judicious organization of the fusion processing and to exploit measurements of the distance between pairs of platforms and inertial measurements. of these platforms to deduce their position, even in the event of high mobility of these platforms.

To this end, the subject of the invention is a process for the geolocation of platforms moving in formation.

The method comprises the following steps implemented each time a set of measurements is acquired, the set of measurements comprising local measurements relating to each of the platforms and distance measurements between each pair of platforms:

- temporal alignment of the measurements of the set of measurements to obtain a prediction of each measurement at a future instant t _k+1 ;

- determination of navigation data relating to all of the platforms at time t _k+1 from the predictions of the measurements at time t _k+1 ;

- updating the predictions of each local measurement at time t _k+1 or of the navigation data relating to all the platforms at time t _k+1 by using a previous state vector comprising relative navigation data to all the platforms at a time t _k past;

- composition of a following state vector from the navigation data relating to all the platforms at time t _k+1 .

According to other advantageous aspects of the invention, the method comprises one or more of the following characteristics, taken in isolation or in all technically possible combinations:

- the navigation data includes the position and speed of each platform at the corresponding time;

- the local measurements relating to each of the platforms include inertial measurements relating to this platform;

- the updating step is implemented for the predictions of each local measurement at time t _k+1 after the time alignment step and before the navigation data determination step; the navigation data relating to all the platforms at time t _k+1 then being determined from the updated predictions of each local measurement at time t _k+1 and from the predictions of each distance measurement at the instant t _k+1 ;

- the updating step is implemented for the navigation data after the step of determining this navigation data and before the step of composing the next state vector; the next state vector then being determined from the updated navigation data;

- the time alignment step comprises the time alignment of the distance measurements using the previous state vector;

- the temporal alignment of the distance measurements comprises for each distance measurement the verification of a condition of instantaneity of this measurement consisting in comparing the product of the measurement time and of a first relative speed of the pair of platforms corresponding to this measurement, with a predetermined threshold, the first relative speed being determined at the instant of this measurement;

- when said product is below the predetermined threshold, the corresponding measurement is considered instantaneous, the prediction of this measurement at time t _k+1 being determined according to this measurement, time t _k+1 , instant of the measurement, of a relative position and a second relative speed of the pair of platforms corresponding to this measurement, the relative position and the second relative speed being determined at the instant t _k from the state vector previous ;

- when said product is greater than or equal to the predetermined threshold, the corresponding measurement is considered as non-instantaneous, the prediction of this measurement at time t _k+1 being determined as a function of time t _k+1 , a first sum, of a second sum, of a relative position and of a second relative speed of the pair of platforms corresponding to this measurement, the relative position and the second relative speed being determined at time t _k from the previous state vector;

the first sum corresponding to the sum of the instant of emission of a signal of predetermined type by one of the platforms of the corresponding pair and of the instant of reception by the platform having emitted the signal of predetermined type from a response signal to this predetermined type signal;

the second sum corresponding to the sum of a first distance separating the platforms substantially at the time of transmission of the predetermined type signal and of a second distance separating the platforms substantially at the time of reception of the response signal to the type signal predetermined, the second sum being advantageously approximated by the product Or :

is the propagation speed of said signals;

is the sum of the propagation times of the signal of predetermined type and of the response signal to this signal; And

- the navigation data determination step comprises the determination of a two-dimensional position of each platform in a horizontal plane and then the determination of a three-dimensional position of each platform by using an altitude measurement of this platform.

The invention also relates to a computer program product comprising software instructions which, when implemented by computer equipment, implement the method as defined above.

The invention also relates to a geolocation module for platforms moving in formation comprising technical means configured to implement the method as defined above.

These characteristics and advantages of the invention will appear on reading the following description, given solely by way of non-limiting example, and made with reference to the appended drawings, in which:

- FIG. 1 is a schematic view of a plurality of platforms moving in formation, each of the platforms comprising a geolocation module according to the invention;

- Figure 2 is a detailed schematic view of one of the geolocation modules of Figure 1;

- FIG. 3 is a flowchart of a geolocation method according to a first embodiment of the invention, the method being implemented by the geolocation module of FIG. 2;

- Figure 4 is a schematic view explaining the implementation of one of the steps of the method of Figure 3.

In fact, FIG. 1 shows a plurality of platforms moving in formation.

As explained above, by "platform" is meant any machine, in particular a motorized machine, capable of moving in space, in particular in formation with other machines.

This formation is composed of N platforms, where N is a natural number greater than or equal to 2.

In the example of FIG. 1, each platform is an aircraft, in particular an airplane, identified in this figure by one of the references A ₁ to A ₄ .

Furthermore, in the example of this figure, the platforms A ₁ to A ₄ perform a formation flight in the shape of a diamond.

This form of training is variable over time depending for example on external events or predetermined rules.

In addition, advantageously, each platform A ₁ to A ₄ has high mobility relative to each other platform. This means in particular that the relative positions of the platforms change rapidly.

Each platform A ₁ to A ₄ includes a geolocation module making it possible to implement collaborative navigation within the training, as will be explained in detail later.

The geolocation modules and components associated with these modules of the platforms A ₁ to A ₄ are for example all analogous to each other. Thus, subsequently, only a navigation module 10 and components associated with it of the platform A ₁ will be explained in detail with reference to Figure 2.

Thus, as can be seen in this figure 2, the geolocation module 10 comprises an input unit 12, a processing unit 13 and an output unit 14.

Each of these units 12 to 14 is at least partially in the form of a programmable logic circuit and/or software configured to implement the associated functions. Moreover, when at least one of these units 12 to 14 is at least partially in the form of software, this software is stored in an associated memory and is implemented by an associated software.

The input unit 12 is able to acquire data from external systems.

In particular, the input unit 12 is able to acquire navigation data from a GNSS sensor 22. These navigation data are deduced from signals transmitted by the satellites of a GNSS system and in particular make it possible to determine a position absolute in a terrestrial reference of the corresponding platform A ₁ .

The input unit 12 is also able to acquire data from a radio communication system 23 with the other training platforms.

In particular, the radio communication system 23 makes it possible to establish a radio link with an analog system of at least one other platform in order to receive useful data from this other platform and to determine telemetry data from this link and advantageously, goniometry data relating to this other platform.

The telemetry data includes in particular distance measurements between the corresponding platforms. These data are deduced for example from the radio link established between the two platforms by sending a signal of a predetermined type in this link and by measuring the response time to this signal by a response signal.

The goniometry data generated by one of the platforms notably includes angle measurements between the other platform and a predetermined direction. These measurements are deduced by analyzing the directions of origin of the radioelectric signals forming the corresponding radioelectric link.

Payload data includes data related to different training platforms.

These payload data include, for example, measurements relating to the absolute position and the altitude of each of the platforms, including platforms without a direct radio link with the platform A ₁ . For this, it is necessary for each of the platforms to have a radio link with at least one other platform. In this case, useful information relating to such a platform is transmitted to all the other platforms via one or more other platforms.

These payload data also include distance measurements between platforms other than platform A ₁ .

Thus, the radiocommunication system 23 makes it possible to establish a meshed communication network within the formation of the platforms A ₁ to A ₄ which makes it possible to transmit useful data relating to all of the platforms.

The input unit 12 also makes it possible to acquire measurements coming from an inertial unit 24 and from an altimeter 25 of the platform A ₁ .

In particular, in a manner known per se, the measurements delivered by the inertial unit 24 include inertial measurements making it possible to deduce an absolute position of the platform A ₁ from a reference point. This absolute position is deduced by analyzing the accelerations of the platform A ₁ detected by the inertial unit 24 from the reference point.

Also in a manner known per se, the measurements delivered by the altimeter 25 include measurements relating to the current altitude of the platform A ₁ .

In the rest of the description, the measurements delivered by the inertial unit 24, by the altimeter 25 and by the GNSS sensor 22 will be called local measurements. Indeed, each local measurement relates to a single platform A ₁ to A ₄ .

Thus, each local measurement corresponds to the position, to the speed, to the acceleration or to the altitude of the corresponding platform A ₁ to A ₄ .

Unlike a local measurement, a distance measurement between a pair of platforms is relative to two platforms.

The processing unit 13 makes it possible to analyze all of the data acquired by the input unit 12 in order to deduce therefrom navigation data relating to each of the platforms A ₁ to A ₄ .

In particular, the processing unit 13 comprises a buffer memory 27 capable of storing data to be processed by the unit 13. A

The processing unit 13 is able to process in one processing cycle all the data stored in this buffer memory 27.

The time span of each processing cycle is for example less than 400 ms, advantageously 200 ms and preferably 100 ms.

The navigation data includes in particular the position and the speed of each of the platforms A ₁ to A ₄ as well as variances associated with the precision of these values.

To determine these data, the processing unit 13 is capable of implementing at least certain steps of a geolocation method explained in detail below.

The output unit 14 is capable of transmitting the navigation data determined by the processing unit 13 to on-board systems of the platform A ₁ which are configured to use these positions.

So, for example, these on-board systems include a traffic alert and collision avoidance system, a navigation system, a display system, etc.

The geolocation method according to a first embodiment of the invention will now be explained with reference to FIG. 3 presenting a flowchart of its steps.

In the example described, this method is implemented by the geolocation module 10 of the platform A ₁ which is then called the reference platform. The other platforms A ₂ to A ₄ are called neighboring platforms.

However, it should be understood that advantageously, the geolocation method described below is implemented by the geolocation module 10 of each of the platforms. Thus, in the general case, the platform implementing the geolocation method is considered as the reference platform for the purposes of this method, the other platforms being considered as neighboring platforms.

Furthermore, it should also be understood that the method described below can be implemented by an external geolocation module of any platform. In this case, such a module, placed for example on the ground, defines a privileged data link with at least one of the platforms A ₁ to A ₄ which is then called in this case reference platform, the other platforms being called platforms neighbours.

It is also assumed that each platform has a radio link with at least one other platform.

Finally, it is assumed that the formation A ₁ to A ₄ is for example in a zone of at least partial interference of the GNSS signals.

During an initial step 110, the input unit 12 acquires all the data from the components 22 to 25 associated with this unit.

These data comprise a set of measurements which is, as described above, composed of local measurements relating to each platform A ₁ to A ₄ and distance measurements between each pair of platforms.

Advantageously, the local measurements relating to each platform A ₁ to A ₄ include the position, the speed and preferably the altitude of this platform.

Then, the input unit 12 transmits the set of measurements to the processing unit 13 which stores them in the buffer memory 27. In other words, during this step 110, the processing module 13 buffers the data to be processed in one processing cycle.

Steps 120 to 150 described below correspond to one processing cycle.

In other words, this processing cycle is implemented by the processing module 13 on each new acquisition of a set of measurements.

It is furthermore assumed that this processing cycle is implemented between a past instant t _k and a future instant t _k+1 .

During step 120, the processing module 13 temporally aligns all the measurements.

For this, the processing module 13 calculates predictions of each measurement at time t _k+1 . These predictions at instant t _k+1 therefore present measurements aligned temporally at instant t _k+1 .

Predictions are calculated differently depending on the nature of the measurements.

Thus, the local measurements are extrapolated at time t _k+1 using techniques known per se.

These techniques assume for example that each platform moves between time t and time t _k+1 along a rectilinear trajectory with a constant speed.

This can for example be done by using a Kalman filter, for example of the NCV type.

Advantageously, the predictions of the distance measurements at time t _k+1 are calculated differently.

In the following, this calculation will be explained for a single distance measurement, for example for a distance measurement between the reference platform A ₁ and one of the neighboring platforms, for example the neighboring platform A ₂ . The calculation of the predictions of the other distance measurements is implemented in an analogous manner.

This calculation is implemented using a previous state vector .

The previous state vector includes navigation data at time t _k for each platform.

The vector includes absolute positions And platforms A ₁ and A ₂ at time t _k as well as the absolute speeds And of these platforms at this same instant t _k .

To calculate the prediction , the processing module 13 first of all examines a condition of instantaneousness of the measurement consisting in comparing the product of the measurement time and a first relative speed platforms A ₁ and A ₂ , with a threshold predetermined.

The first relative speed is for example determined according to the following relationship:

Or And are measurements of the speed respectively of platforms A ₁ and A ₂ at time t.

The predetermined threshold is for example equal to Or is the maximum variance that we tolerate on the measure .

When said product is below the predetermined threshold, i.e. when , the measure is considered instantaneous. In other words, in this case, the relative mobility of the two platforms remains compatible with the maximum tolerated variance.

In this case, the prediction of this measurement at time t _k+1 is determined as a function of this measurement, of time t _k+1 , of time t, of a relative position of the platforms and of a second relative speed of the platforms A ₁ and A ₂ .

In particular, the prediction is determined as follows:

where the relative position is determined according to the following expression:

and the second relative speed is determined according to the following expression:

When said product is greater than or equal to the predetermined threshold , that is, when , the measure is considered non-instantaneous.

In particular, in this case, it is considered that the response time to the signal of the predetermined type by one of the platforms is non-negligible compared to the relative movement of the platforms.

Such a case is schematically illustrated in Figure 4.

Indeed, FIG. 4 illustrates a time scale t during the radioelectric communication of the platforms A ₁ and A ₂ .

It is considered on this scale that the platform A ₁ sends a signal of the predetermined type S ₁ at the instant TAtx. This signal is received by platform A ₂ at time TRtx.

Then, platform A ₂ sends a response signal S ₂ at time TRtx which is received by platform A ₁ at time TRrx.

In the example of this figure 4, the difference TRtx-TArx corresponds to the response time by the platform A ₂ and cannot be neglected with respect to the relative displacement of the platforms A ₁ and A ₂ during the measurement time , that is to say during the time interval equal to TRrx-TAtx.

Thus, when the measure is considered non-instantaneous, its prediction is determined as a function of the instant t _k+1 , of a first sum, of a second sum, of the relative position and the second relative speed platforms A ₁ and A ₂ .

The first sum corresponds to the sum of the TAtx and TRrx values which are also measured by each of the platforms and are transmitted with the corresponding distance measurements.

The second sum corresponds to the sum of a first distance separating the platforms substantially at the time of transmission of the predetermined type signal S ₁ and by a second distance separating the platforms substantially at the time of reception of the response signal S ₂ to the signal of predetermined type S ₁ .

In particular, the prediction is determined as follows:

Or

is the first sum then equal to TAtx+TRrx; And

is the second sum.

According to the invention, this second sum is equal to the product Or :

is the propagation speed of the signals S ₁ and S ₂ ;

is the sum of the propagation times of the signal of predetermined type S ₁ and of the response signal to this signal S ₂ .

The value is calculated by subtracting the response time to the signal of predetermined type S ₁ from the total measurement time. In other words, this value is equal to (TRrx-TAtx)-(TRtx-TArx).

The response time TRtx-TArx to a signal is specific to each of the platforms A ₁ to A ₄ . This response time is known because transmitted for example with the response signal S ₂ for each distance measurement between the pair of corresponding platforms.

During the next step 130, the processing unit 13 updates the predictions of each local measurement at time t _k+1 using the previous state vector .

This step therefore corresponds to the merging of the navigation data known at time t_kwith the predictions of each local measurement at time t_k+1 and aims to improve the accuracy of predictions of local measurements at time t_k+1.

This fusion is carried out according to techniques known per se.

During the next step 140, the processing unit 13 determines navigation data relating to all of the platforms at time t _k+1 from the predictions of the distance measurements at time t _k+1 and updated predictions of local measurements at time t _k+1 .

In particular, during this step, the processing unit 13 uses the absolute positions of each of the platforms and the distances between each pair of platforms to obtain precise absolute positions of each of the platforms.

To do this, the processing module 13 uses for example a technique known per se and usually used in the field of collaborative geolocation.

According to a particular embodiment of the invention, to determine precise positions of each platform, the processing unit 13 first projects the absolute positions of the platforms which are known from the updated predictions of the local measurements at the instant t _k+1 , on a horizontal plane. This horizontal plane is for example defined by the reference platform A ₁ .

Then, the processing module 13 determines an image in this horizontal plane of the prediction of each distance measurement at time t _k+1 . Such an image corresponds for example to the orthogonal projection of a vector of length equal to said prediction and direction defined by the absolute positions of the corresponding platforms.

Then, the processing module 13 determines two-dimensional positions of each platform in the horizontal plane by using the projections of the known absolute positions of these platforms and the images of the predictions of the distance measurements in this horizontal plane.

Finally, to obtain three-dimensional positions of each platform, the processing module 13 supplements the two-dimensional positions obtained by the altitudes of these platforms. These altitudes are also obtained from the updated predictions of the local measurements at time t _k+1 .

During the next step 150, the processing unit 13 finalizes the processing cycle by defining a next state vector from the navigation data obtained during the previous step 140.

Thus, during the next processing cycle, this next state vector will be considered as the previous state vector and a new next state vector will then be obtained at the end of this cycle. Then, a new processing cycle is again implemented.

In step 160, the output unit 14 transmits each next new state vector to the corresponding on-board systems which use the navigation data relating to all the platforms in accordance with their functionalities.

The geolocation method according to a second embodiment differs from that according to the first embodiment by the order of execution of the steps.

In particular, according to the second embodiment, the step 140 for determining the navigation data is implemented before the step 130 for updating the predictions of the local measurements.

In this case, during step 140, the processing unit 13 determines navigation data relating to all of the platforms at time t _k+1 from the predictions of the distance measurements at time t _k+1 and non-updated predictions of local measurements at time t _k+1 , as explained above.

Then, the processing module 13 implements the step 130 during which it updates the navigation data obtained during the step 140 by using the state vector previous as explained above.

Finally, the processing module 13 implements the step 150 during which it composes the following state vector based on updated navigation data.

It can then be seen that the invention has a certain number of advantages.

First of all, the invention makes it possible to obtain navigation data from platforms moving in formation in a very precise manner, even in the event of very high mobility of these platforms.

This is achieved in particular by implementing a time alignment of all measurements and by using accurate predictions of distance measurements between different pairs of platforms. These predictions notably take into account the relative displacements between the platforms when taking measurements.

Finally, by processing two-dimensional positions in a horizontal plane instead of three-dimensional positions, the implementation of each processing cycle according to the method can be considerably accelerated. Thus, it is possible to process more measurements with the same performance of the geolocation module, which further improves the accuracy of the results.

Claims (12)

Geolocation process for platforms (A ₁ ,…, A ₄ ) moving in formation;
the method comprising the following steps implemented at each acquisition of a set of measurements, the set of measurements comprising local measurements relating to each of the platforms (A ₁ ,…, A ₄ ) and distance measurements between each pair of platforms:
- time alignment (120) of the measurements of the set of measurements to obtain a prediction of each measurement at a future instant t _k+1 ;
- determination (140) of navigation data relating to all of the platforms (A ₁ ,…, A ₄ ) at time t _k+1 from the predictions of the measurements at time t _k+1 ;
- updating (130) the predictions of each local measurement at time t _k+1 or of the navigation data relating to all the platforms (A ₁ ,…, A ₄ ) at time t _k+1 using a previous state vector ( ) comprising navigation data relating to all of the platforms (A ₁ ,…, A ₄ ) at a time t _k past;
- composition (150) of a following state vector ( ) from the navigation data relating to all of the platforms (A ₁ ,…, A ₄ ) at time t _k+1 . Method according to claim 1, wherein the navigation data comprises the position and the speed of each platform (A ₁ ,…,A ₄ ) at the corresponding instant. Method according to claim 1 or 2, in which the local measurements relating to each of the platforms (A ₁ ,…,A ₄ ) comprise inertial measurements relating to this platform (A ₁ ,…,A ₄ ). A method according to any preceding claim, wherein the updating step (130) is implemented for the predictions of each local measurement at time t _k+1 after the time alignment step (120 ) and before the step of determining (130) the navigation data;
the navigation data relating to all of the platforms (A ₁ ,…,A ₄ ) at time t _k+1 then being determined from the updated predictions of each local measurement at time t _k+1 and at from the predictions of each distance measurement at time t _k+1 . Method according to any one of Claims 1 to 3, in which the step of updating (130) is implemented for the navigation data after the step of determining (140) this navigation data and before the composition step (150) of the next state vector ( );
the next state vector ( ) being then determined from the updated navigation data. A method as claimed in any preceding claim, wherein the step of time aligning (120) comprises time aligning the distance measurements using the previous state vector ( ). Method according to claim 6, in which the time alignment of the distance measurements comprises for each distance measurement the verification of a condition of instantaneity of this measurement consisting in comparing the product of the measurement time ( ) and a first relative speed ( ) of the pair of platforms corresponding to this measurement, with a predetermined threshold ( ), the first relative speed ( ) being determined at the instant of this measurement. A method according to claim 7, wherein when said product is below the predetermined threshold ( ), the corresponding measurement is considered instantaneous, the prediction of this measurement at time t _k+1 being determined as a function of this measurement, time t _k+1 , time of measurement, a relative position and a second relative speed of the pair of platforms corresponding to this measurement, the relative position and the second relative speed being determined at time t _k from the previous state vector ( ). Method according to claim 7 or 8, wherein when said product is greater than or equal to the predetermined threshold ( ), the corresponding measurement is considered as non-instantaneous, the prediction of this measurement at instant t _k+1 being determined as a function of instant t _k+1 , of a first sum, of a second sum, a relative position and a second relative speed of the pair of platforms corresponding to this measurement, the relative position and the second relative speed being determined at time t _k from the previous state vector ( );
the first sum corresponding to the sum of the instant of transmission of a signal of predetermined type ( ) by one of the platforms of the corresponding pair and of the instant of reception by the platform having transmitted the signal of the predetermined type of a response signal ( ) to this predetermined type signal;
the second sum corresponding to the sum of a first distance ( ) separating the platforms substantially at the time of transmission of the signal of predetermined type ( ) and a second distance ( ) separating the platforms substantially at the time of receipt of the response signal ( ) to the signal of predetermined type, the second sum being advantageously approximated by the product Or :
is the propagation speed of said signals;
is the sum of the propagation times of the signal of predetermined type and of the response signal to this signal. A method according to any preceding claim, wherein the step of determining (140) the navigation data comprises determining a two-dimensional position of each platform (A ₁ ,…,A ₄ ) in a horizontal plane and then , the determination of a three-dimensional position of each platform (A ₁ ,…,A ₄ ) by using an altitude measurement of this platform (A ₁ ,…,A ₄ ). Computer program product comprising software instructions which, when implemented by computer equipment, implement the method according to any of the preceding claims. Geolocation module (10) of platforms (A ₁ ,…, A ₄ ) moving in formation comprising technical means (12, 13, 14, 27) configured to implement the method according to any one of claims 1 to 10.